If the function `f: RR rarr RR` be defined by, `f(x)={(x " when "x in QQ ),(1-x " when " x in QQ ):}`
then prove that , `(f o f)=I_(RR)`.

Let, the function f:RRrarrRR be defined by, f(x)={:{(1 ,"when " x in QQ),(-1,"when "x !in QQ):}" find" range of f

Let RR and QQ be the sets of real numbers and rational numbers respectively. If a in QQ and f: RR rarr RR is defined by , f(x)={(x " when" x in QQ ),(a-x" when " x notin QQ ):} then show that , (f o f ) (x) = x , for all x in RR

Let, the function f:RRrarrRR be defined by, f(x)={:{(1 ,"when " x in QQ),(-1,"when "x !in QQ):}" find" pre-image of 1 and (-1)

Let, the function f:RRrarrRR be defined by, f(x)={:{(1 ,"when " x in QQ),(-1,"when "x !in QQ):}" Find" f(2),f(sqrt(2)),f(pi),f(2.23),f(e)

Prove that, the function f: RR rarr RR defined by f(x)=x^(3)+3x is bijective .

If the function f: R to R is defined by f(x) =(x^(2)+1)^(35) for all x in RR then f is

Let the function f:RR rarr RR be defined by f(x)=x^(2) (RR being the set of real numbers), then f is __

Let t the function f:RR to RR be defined by, f(x)=a^x(a gt0 ,a ne1). Find range of f

Let f: RR rarr RR be defined by f(x)={(|x|/(x) " when " x ne 0 ),(0" when "x =0 ):} and the function g: RR rarr RR be defined by g(x) =[x] where [x] is the greatest integer function. Prove that the functions (f o g) and (g o f) are same in [-1,0).

Let the function f:RR rarr RR and g:RR be defined by f(x) = sin x and g(x)=x^(2) . Show that, (g o f) ne (f o g) .